Nonlinear Equation: Solve x,y,z

[dirk_mec1]

Homework Statement

Solve x,y and z from $$\frac{y+z}{a}= \frac{x+z}{b}=\frac{x+y}{c} = xyz$$

wit a,b,c not equal to zero.

Homework Equations

The Attempt at a Solution

I have no idea how to start. I've tried several things but it seems like I'm missing something. I did find the trivial solution (0,0,0).

 

[Ray Vickson]

Homework Statement

Solve x,y and z from $$\frac{y+z}{a}= \frac{x+z}{b}=\frac{x+y}{c} = xyz$$

wit a,b,c not equal to zero.

Homework Equations

The Attempt at a Solution

I have no idea how to start. I've tried several things but it seems like I'm missing something. I did find the trivial solution (0,0,0).

You say you tried several things. What were they? You need to show your work.

 

[Saitama]

Homework Statement

Solve x,y and z from $$\frac{y+z}{a}= \frac{x+z}{b}=\frac{x+y}{c} = xyz$$

wit a,b,c not equal to zero.

Homework Equations

The Attempt at a Solution

I have no idea how to start. I've tried several things but it seems like I'm missing something. I did find the trivial solution (0,0,0).

Rewrite the equation as
$$\frac{1}{a}\left(\frac{1}{xz}+\frac{1}{xy}\right)=\frac{1}{b} \left( \frac{1}{yz}+\frac{1}{xy}\right)=\frac{1}{c}\left(\frac{1}{yz}+\frac{1}{xz}\right)=1$$
Substitute $1/(xy)=p, 1/(yz)=q$ and $1/(xz)=r$. Form three equations to find p, q and r. This gives the possible non-zero solutions.

 

[dirk_mec1]

Understood, thanks.